PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
80012^186713+7681756207Enzo Doria05/2016
800216534^2505+2505^1653456196Hans Havermann06/2016
800314428^7849+7849^1442856195Hans Havermann06/2016
800414898^5909+5909^1489856189Hans Havermann06/2016
800518^44758+9556184Lelio R Paula02/2013
80062^186555-74156159Lelio R Paula05/2011
8007(4*10^56156+173)/356157Robert Price01/2017
8009(3^117708+7)/44789656156Lelio R Paula03/2012
800815711^3752+3752^1571156156Hans Havermann06/2016
8010(23*2^186549-1)/242902556152Lelio R Paula01/2014
8011387^21694+21694^38756138Norbert Schneider08/2014
80122^186422+1723956119Yves Minet01/2010
80132^186418+424242956118Jason Earls10/2008
8014136^26300+13556113Norbert Schneider04/2015
80155*2^186392+956111Lelio R Paula03/2014
801614345^8152+8152^1434556108Hans Havermann07/2016
8017(5*2^186351-1)/3956097Lelio R Paula01/2014
80182^186319-54123756088Paul Bourdelais11/2012
8019(16*10^56082-61)/956083Serge Batalov05/2009
8020(14*10^56080-143)/356081Robert Price01/2017
8021(265*10^56076+17)/356078Robert Price05/2016
80227^66346-5056069Lelio R Paula10/2012
802320^43094-3356067Lelio R Paula02/2013
802420^43090-138356062Enzo Doria03/2013
80253^117482+266056054Lelio R Paula10/2012
8026(22699*2^186193+1)/11156052Lelio R Paula05/2014
8027(68*10^56042+13)/956043Ray Chandler09/2010
80283*6^71992+5^7199256022Mike Oakes03/2010
802913691^12352+12352^1369156020Hans Havermann07/2016
8030(2^186095+7)/7556019Lelio R Paula02/2012
8031247^23412+23412^24756018Norbert Schneider08/2014
80321839^17156+17156^183956008Serge Batalov05/2014
803313736^11949+11949^1373656007Hans Havermann04/2016
8034(5*2^186036-1)/1156003Lelio R Paula01/2014
8035(299*10^55998-17)/356000Robert Price01/2017
8036p(12103)#/2-12855994Robert Price05/2017
80382^186003-17433755993Gary Barnes09/2009
8037(2^186010+78557)/12355993Lelio R Paula05/2012
803920^43037-9355993Lelio R Paula02/2013
804016375^2626+2626^1637555991Hans Havermann03/2016
804115631^3816+3816^1563155985Hans Havermann03/2016
804221^42335-255977Lelio R Paula08/2013
8043Phi(64736,139)55959Enzo Doria07/2012
804415215^4762+4762^1521555958Hans Havermann03/2016
804519317^788+788^1931755953Anatoly F. Selevich12/2006
804613582^13165+13165^1358255950Hans Havermann08/2016
8047(78557*2^185842+1)/18955947Lelio R Paula06/2014
804815^47562-8655938Lelio R Paula02/2013
80493^117222+455930Lelio R Paula03/2012
805024^40519-23^4051955925Robert Price07/2012
805113636^12623+12623^1363655924Hans Havermann07/2016
80522^185767-9955922Lelio R Paula03/2011
8053(19*2^185750-1)/1555917Lelio R Paula01/2014
805415^47542-5855914Lelio R Paula02/2013
805520^42973-558355910Enzo Doria03/2013
80564*10^55906+2155907Robert Price08/2016
80572^185713-11155906Lelio R Paula03/2011
805813^50174+8855891Lelio R Paula01/2013
805914569^6846+6846^1456955879Hans Havermann08/2016
8060Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
80613^117087-8055865Lelio R Paula10/2012
8062(7*10^55851-43)/955851Robert Price10/2014
80632^185519-16955847Lelio R Paula03/2011
80647^66074+1055840Lelio R Paula10/2012
8065(19*10^55833-49)/355834Robert Price02/2017
8066(2*10^55834-59)/355834Robert Price05/2017
806712^51732+555829Lelio R Paula01/2013
80683*2^185429+755821Lelio R Paula03/2014
8069(9787*2^185420-1)/38155819Lelio R Paula04/2015
807014427^7396+7396^1442755819Hans Havermann08/2016
807110^55811+2155812Robert Price01/2011
807210^55811-7410355811Patrick De Geest12/2012
807311^53591-153055810Enzo Doria11/2012
80742^185355-214555798Lelio R Paula03/2011
807514531^6912+6912^1453155794Hans Havermann07/2016
80762^185327-161555789Lelio R Paula03/2011
80772^185280-1277955775Enzo Doria10/2012
807815504^3955+3955^1550455771Hans Havermann07/2016
8079(2*10^55762-59)/355762Robert Price05/2017
80805^79770-4455757Lelio R Paula10/2012
808118^44416-8555755Lelio R Paula02/2013
80822^185208-45999555754Enzo Doria06/2015
80832^185200+118555751Lelio R Paula03/2011
80847^65964+6^(65964-1)55747Robert Price03/2016
80852^185151-23715755737Gary Barnes09/2009
8086110017^11055-10255734Enzo Doria07/2012
808714754^5987+5987^1475455729Hans Havermann07/2016
808840090!3-955711Robert Price09/2014
80899*10^55707+8955708Robert Price11/2016
80902^185023-225755698Yves Minet06/2009
809118628^977+977^1862855696Anatoly F. Selevich01/2007
80922^185006-9355693Lelio R Paula03/2011
80932^185003-251555692Yves Minet07/2014
80946^71524-1955657Lelio R Paula10/2012
80952^184872-219555653Yves Minet08/2013
8096507^20572+20572^50755648Norbert Schneider06/2016
8097134^26151-13355626Norbert Schneider03/2015
809815340^4221+4221^1534055614Hans Havermann07/2016
809927743!2+255612Robert Price01/2013
810020^42744+8155612Lelio R Paula02/2013
810114609^6406+6406^1460955611Hans Havermann07/2016
81022^184724-11288355608Enzo Doria06/2014
810313507^13074+13074^1350755601Hans Havermann07/2016
81042^184689+12955597Lelio R Paula03/2011
8105(9179*2^184672-1)/19355594Lelio R Paula03/2015
8106(22*10^55592-19)/355593Robert Price02/2017
8107Phi(59984,89)55582Enzo Doria05/2012
810811^53368+1655578Lelio R Paula01/2013
810920^42717-192355577Enzo Doria03/2013
8110117^26870+26870^11755573Serge Batalov05/2014
811112^51488+5555565Lelio R Paula01/2013
8112(44*10^55558-17)/955559Robert Price06/2015
811310^55555+3285755556Patrick De Geest06/2010
811410^55555-13672155555Patrick De Geest06/2010
8115(11*2^184541-1)/35155551Lelio R Paula01/2014
811620^42696-204355549Enzo Doria03/2013
8117(2*10^55544+1)/355544Serge Batalov06/2009
8118(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
81195003^15013-16055537Enzo Doria07/2012
812039^34896-255522Lelio R Paula08/2013
8121(6^71345-61)/555517Lelio R Paula05/2014
81222^184407-301955513Yves Minet10/2014
8123(43*10^55512-61)/955513Robert Price06/2015
812420^42667-84355512Enzo Doria03/2013
8125133^26134-13255505Norbert Schneider03/2015
8126(31*2^184378-1)/71155502Lelio R Paula01/2014
81279*7^65667-455497Lelio R Paula09/2014
81282^184342-17355493Lelio R Paula03/2011
812915^47182+9255491Lelio R Paula02/2013
81305^79378+655483Lelio R Paula10/2012
8131581^20068+20068^58155472Norbert Schneider06/2016
8132(2^184232+1)/25755457Donovan Johnson03/2005
813318^44177-141555455Enzo Doria03/2013
81342^184203-279786755451Enzo Doria04/2016
81352^184189+1755447Lelio R Paula03/2011
81362^184183+2612355445Yves Minet01/2010
8137Phi(77077,10)55441Ray Chandler05/2009
81382^184141-11325155432Enzo Doria07/2014
81392^184093-50461355418Gary Barnes09/2009
8140(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
81412^184044-11126955403Enzo Doria05/2014
814214051^8766+8766^1405155401Hans Havermann07/2016
814398^27819+27819^9855394Serge Batalov05/2014
814458046^9+9^5804655390Andrey Kulsha02/2004
81452^183980+7524155384Enzo Doria04/2016
814610^55372+3755373Robert Price01/2011
814710^55372-4996755372Patrick De Geest12/2012
8148(13*10^55367+17)/355368Robert Price06/2015
81492*6^71150+755366Lelio R Paula09/2014
815019^43296-6255365Lelio R Paula02/2013
815119^43295+1055364Lelio R Paula02/2013
8152(29*10^55362-11)/955363Robert Price04/2015
8153(37*10^55359+53)/955360Robert Price05/2015
815419^43283+7255349Lelio R Paula02/2013
81552^183800-6555330Lelio R Paula03/2011
815621001^12801-11055329Enzo Doria07/2012
815733^36433-32^3643355325Robert Price04/2012
8158(17*2^183729+1)/14555308Lelio R Paula07/2012
81609^57952+8^(57952-1)55301Robert Price03/2016
815914872^5229+5229^1487255301Hans Havermann08/2016
816161^30972-255296Lelio R Paula08/2013
81622^183671-11253755291Enzo Doria06/2014
8163(2^183687+7)/49793974555287Lelio R Paula02/2012
81643^115873+5655286Lelio R Paula10/2012
816513^49629-8455284Lelio R Paula01/2013
81662^183632-555279Henri Lifchitz08/2005
816713981^8988+8988^1398155277Hans Havermann07/2016
8168(5*2^183585+1)/1355265Lelio R Paula07/2012
81692^183576+17155262Lelio R Paula03/2011
817013^49604+8255257Lelio R Paula01/2013
8171(11*10^55254+1)/355255Erik Branger03/2014
81723^115802-2655252Lelio R Paula10/2012
81732^183534-364555250Lelio R Paula01/2011
8174(15*2^183533-1)/11355249Lelio R Paula01/2014
81755^79032-1376655241Enzo Doria02/2013
81768*3^115759-755232Lelio R Paula03/2014
81776^70974-13755229Lelio R Paula10/2012
81782^183446-11307355223Enzo Doria07/2014
81792^183441+57729457555222Lelio R Paula03/2013
81805^79000-655219Lelio R Paula10/2012
81812^183413-90155213Yves Minet01/2012
818219^43168-5055202Lelio R Paula02/2013
81832^183340+1968355191Lelio R Paula02/2012
81846^70923+3555189Lelio R Paula10/2012
81852^183317-403555184Lelio R Paula01/2011
81862^183284-1555174Lelio R Paula03/2011
81872^183255+14955166Lelio R Paula02/2011
81884*10^55165+8755166Robert Price05/2016
8189(3^115574+4)/6303755139Lelio R Paula03/2012
81902^183165-11233355139Enzo Doria06/2014
81912^183142+85555132Lelio R Paula01/2011
8192(49*10^55129+383)/955130Robert Price04/2017
81932^183019+25525555095Lelio R Paula01/2011
81943*10^55077+755078Erik Branger11/2013
8195(62*10^55075-71)/955076Robert Price09/2015
819627499!2-3255070Robert Price10/2015
819715307^3958+3958^1530755067Hans Havermann08/2016
819870^29836-6955051Norbert Schneider10/2012
819918^43854-8355049Lelio R Paula02/2013
82007^65126+5855038Lelio R Paula10/2012
82012^182827-161555037Lelio R Paula11/2009
82027*10^55030-955031Dmitry Domanov11/2010
82036^70702+2355017Lelio R Paula10/2012
8204(23*2^182753+1)/15155014Lelio R Paula07/2012
82052^182743-161555012Lelio R Paula11/2009
8206(24737*2^182736+1)/39955011Lelio R Paula05/2014
82073^115280-956855003Enzo Doria02/2013
82082^182656-1284954985Enzo Doria10/2012
82099*19^42995+1654981Curtis Bright05/2015
82102^182627+2842554977Lelio R Paula11/2009
82112^182597-11305354968Enzo Doria07/2014
8212(3^115213+2)/3090672554964Lelio R Paula03/2012
82132^182581-197554963Yves Minet09/2012
821427449!!-1654959Robert Price06/2015
82164^91283-3^9128354958Jean-Louis Charton01/2004
82152^182565+10754958Lelio R Paula11/2009
82172^182560+205354957Lelio R Paula12/2010
82182^182451-18245154924Henri Lifchitz10/2004
82192^182444+8154922Henri Lifchitz10/2005
82202^182433+7410554918Enzo Doria04/2016
822120^42206-524354912Enzo Doria03/2013
82222^182394+8554907Lelio R Paula02/2011
82232^182374-11228754901Enzo Doria06/2014
8224(47^32833-33^32833)/1454899Serge Batalov12/2016
82252^182363-11316754897Enzo Doria07/2014
82262^182359-11222154896Enzo Doria06/2014
8227(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8228(17*2^182274+1)/146754869Lelio R Paula01/2012
822918^43698-554853Lelio R Paula02/2013
82302^182209-189354851Yves Minet09/2012
82312^182194-344354846Yves Minet12/2016
823215023^4468+4468^1502354836Hans Havermann08/2016
82332^182135+9014354829Yves Minet10/2010
82342^182119+7433354824Enzo Doria04/2016
823514289^6860+6860^1428954818Hans Havermann08/2016
82363^114892-114892^354818Norbert Schneider03/2017
82372^182070-4735554809Lelio R Paula01/2011
82383^114869+7654807Lelio R Paula10/2012
82398^60681-60681^854801Norbert Schneider12/2016
82401897^16710+16710^189754777Serge Batalov05/2014
8241Phi(61868,59)54776Enzo Doria04/2012
8242113^26679+254775Lelio R Paula05/2013
82433^114789-7454769Lelio R Paula10/2012
824415^46567+9854768Lelio R Paula02/2013
8245(2*10^54767-71)/354767Robert Price01/2017
8246(298*10^54765-7)/354767Robert Price06/2017
8247(21*2^181931-1)/16999754763Lelio R Paula01/2014
82482^181913+2954762Henri Lifchitz06/2005
8249(31*10^54761-121)/954762Robert Price06/2016
82502^181887+18954754Lelio R Paula02/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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